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Search: MSC category 11R27 ( Units and factorization )

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1. CJM 2004 (vol 56 pp. 71)

Harper, Malcolm; Murty, M. Ram
Euclidean Rings of Algebraic Integers
Let $K$ be a finite Galois extension of the field of rational numbers with unit rank greater than~3. We prove that the ring of integers of $K$ is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions. We now prove this unconditionally.

Categories:11R04, 11R27, 11R32, 11R42, 11N36

2. CJM 2002 (vol 54 pp. 1305)

Vulakh, L. Ya.
Continued Fractions Associated with $\SL_3 (\mathbf{Z})$ and Units in Complex Cubic Fields
Continued fractions associated with $\GL_3 (\mathbf{Z})$ are introduced and applied to find fundamental units in a two-parameter family of complex cubic fields.

Keywords:fundamental units, continued fractions, diophantine approximation, symmetric space
Categories:11R27, 11J70, 11J13

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